As is well known in the art of marine seismic surveying, a sound source is towed behind a ship beneath the surface of a body of water. The sound may be generated by a small explosive charge, an electric spark or arc, a vibrator or, usually, an array of several air guns. The air gun array is towed about 6 to 10 meters beneath the sea surface. The air guns each contain a volume of air compressed to high pressure. Upon command, the guns abruptly release their volumes of compressed air to create a sound wave in the water. The resulting pressure wavefield propagates downwardly, into the earth beneath the sea floor, to the sub-bottom strata, whence the wavefield is reflected back up towards the water surface. The reflected wavefield is detected by a hydrophone array that is towed behind the ship just beneath the water surface. The hydrophone array may extend three thousand meters or more behind the ship and may include up to several thousand hydrophones. The detected reflected wavefields are recorded on time-scale recordings or seismograms.
When the seismic source is triggered or fired, it produces a complex output pressure pulse. Typically, the pulse consists of a short, initial, fast positive rise in amplitude, followed by several rapidlydecaying oscillations. The wavetrain might be 150 to 500 milliseconds (ms) long and is termed the "signature" of the sound source. The wavefield generated by the sound source radiates in all directions and the pulse shape generally varies with distance and direction.
The far field can be defined as that distance from the source at which the amplitude ratio between ghost, i.e. reflection of the wavefield from the water/air interface, and the direct wavefield equals or exceeds 0.95. Another way of defining the far-field is by looking at the distance at which the pressure pulse of the source may without great error be regarded as stemming form an ideal source unchanging with distance in any given direction. Thus, generally the pressure pulse can be represented as a function of position (in polar co-ordinates) and time, i.e. p(r,.theta.,.phi.,t). If the distance, r, is sufficiently large as compared to the characteristic length D, typically the length of the (linear) array, this may be simplified to a far-field approximation in which the dependence on the distance, r, takes a particularly simple form: p(r,.theta.,.phi.,t)=S(.theta.,.phi.,t-r/c)/r.
The salient feature of this far-field approximation is that if r is varied while the polar angles .theta. and .phi. are held constant, the shape of the pressure pulse does not change except in amplitude (as 1/r) and arrival time (delay t/c). Typically the far-field region is considered to begin when this approximation shows an error of about 5%. For all practical purposes, the far-field is considered to exist at distances in excess of 250-300 meters from the source. Under less stringent conditions, the far-field may be allowed to start at about 100 meters from the source.
The far-field signature is either measured by hydrophones located in an appropriate distance from the source or, more conveniently extrapolated from near-field experiments.
In the near-field region, the distances between single elements of the source are of the same order as the distance to the (near-field) receiver. Each receiver must be placed within a distance D from the source array, where D is equal to the largest linear dimension (characteristic length) of the array itself (including the images in the sea surface).Hence, for a marine seismic array that is 15 meters long and 6 meters deep under the surface, the near-field region extends to a depth of about 21 meters.
One method of extrapolating the far-field from the near-field is taught by the U.S. Pat. No. 4,658,384. Another reference of interest is U.S. Pat. No. 4,648,080, issued 03103'87 to N. D. Hargeaves. Other references of interest are U.S. Pat. No. 4,644,507 issued to A. M. Ziolkowski.
In U.S. Pat. No. 4,658,384 the far-field pressure signature of an air-gun array is derived from near-field measurements. An array of air guns is deployed in the water at a desired depth. A hydrophone is suspended in the middle of the array at the same depth so that the guns are equidistant from the hydrophone. The lateral spacing between the guns and the sensor is much less than the water depth of the guns. Having fired the guns, the ghost reflection amplitude in the near field will be much less than the amplitude of the direct arrivals and can be ignored. The far-field signature is determined by inverting the observed pressure signature, delaying it in proportion to array depth and adding the inverted, delayed signature back to the original signature.
In U.S. Pat. No. 4,693,336 a second "calibration" source is fired immediately before the main source. Using the recordings of both sources, the far-field of the main source can be calculated.
Of particular interest are European Patent Application EP-A-0,066,423, which describes an example of air gun array with signature measurement, U.S. Pat. No. 4,908,801 and European Patent Application EP-A-0,555,148.
In U.S. Pat. No. 4,908,801, use is made of a library of stored near-filed source signatures for individual air guns. During the survey, time, position and other environmental parameters are measured for each source and the composite far-field signature of the array is then determined by combining the measured parameters with the individual source signatures as stored in the library.
Use of pre-recorded data is also described in the European Patent Application EP-A-0,555,148, where the far-field signature of an array is recorded by a far-field hydrophone prior to the seismic survey. A transfer function is derived from the pre-recorded data so that the far-field signature can be estimated during the survey using near-field signature alone.
In view of the above cited references, it is seen as an object of this invention to provide methods and apparatus for estimating the signature of a plurality of seismic. More specifically, it is an object of the invention to provide such methods and apparatus to enable real-time estimation of the far-field signature of an seismic source array, particularly where a direct far-field measurement is not possible.